Nope- no mention of them, in fact you did no specify the activity at all.
You have described a single incident where an accident has happened, so let's take your scenario and make it specific to the two groups and ask a simple question??
We have someone in mid air about to strike a rock with their head.
You are out hill walking and trip .....your head is under the force of gravity, heading towards a sharp rock, would you prefer to have some plastic/polystyrene/anything wrapped around your head than my soft skull being exposed.
You are out mountain biking and lose control .....your head is under the force of gravity, heading towards a sharp rock, would you prefer to have some plastic/polystyrene/anything wrapped around your head than my soft skull being exposed.
Your original scenario is precisely the same for both... are you suggesting that hitting the same rock with the same impact is somehow bizarrely not going to hurt as much, or cause the same damage to a hill walker as a mountain biker?
In the specific case you describe surely a helmet would be offer the same level protection in both cases in both cases?
I would love to hear your opinion.